Pattern formation mechanisms of self-organizing reaction-diffusion systems

Embryonic development is a largely self-organizing process, in which the adult body plan arises from a ball of cells with initially nearly equal potency. The reaction-diffusion theory first proposed by Alan Turing states that the initial symmetry in embryos can be broken by the interplay between two diffusible molecules, whose interactions lead to the formation of patterns. The reaction-diffusion theory provides a valuable framework for self-organized pattern formation, but it has been difficult to relate simple two-component models to real biological systems with multiple interacting molecular species. Recent studies have addressed this shortcoming and extended the reaction-diffusion theory to realistic multi-component networks. These efforts have challenged the generality of previous central tenets derived from the analysis of simplified systems and guide the way to a new understanding of self-organizing processes. Here, we discuss the challenges in modeling multi-component reaction-diffusion systems and how these have recently been addressed. We present a synthesis of new pattern formation mechanisms derived from these analyses, and we highlight the significance of reaction-diffusion principles for developmental and synthetic pattern formation.

Development: Painting Flowers with MYBs

Color patterns influence how attractive flowers are to bees, butterflies, and birds. By combining experiments and theory, a new study shows how a pair of MYB transcription factors orchestrates the formation of pigmentation patterns on monkeyflowers.

Remembering where we are: Positional information in salamander limb regeneration

Fifty years ago, Lewis Wolpert defined an important question in developmental biology: how are cell fates determined by the positions of cells within a system? He proposed that cells retain positional values as if they lie within a coordinate system and that the interpretation of these values produces patterns in development. He referred to this concept as positional information. Though initially controversial, this concept of positional information has proven to be profoundly influential in developmental biology. One area in which the influence of Wolpert's theoretical work can be clearly demonstrated is the study of limb regeneration in salamanders. Here, we review the work in limb regeneration leading up to Wolpert defining the concept of positional information and how his theory has guided regeneration research over the subsequent 50 years.

Positional information and tissue scaling during development and regeneration

In order to contribute to the appropriate tissues during development, cells need to know their position within the embryo. This positional information is conveyed by gradients of signaling molecules, termed morphogens, that are produced in specific regions of the embryo and induce concentration-dependent responses in target tissues. Positional information is remarkably robust, and embryos often develop with the correct proportions even if large parts of the embryo are removed. In this Review, we discuss classical embryological experiments and modern quantitative analyses that have led to mechanistic insights into how morphogen gradients adapt, scale and properly pattern differently sized domains. We analyze these experimental findings in the context of mathematical models and synthesize general principles that apply to multiple systems across species and developmental stages.

Rhythmicity and waves in the cortex of single cells

Emergence of dynamic patterns in the form of oscillations and waves on the cortex of single cells is a fascinating and enigmatic phenomenon. Here we outline various theoretical frameworks used to model pattern formation with the goal of reducing complex, heterogeneous patterns into key parameters that are biologically tractable. We also review progress made in recent years on the quantitative and molecular definitions of these terms, which we believe have begun to transform single-cell dynamic patterns from a purely observational and descriptive subject to more mechanistic studies. Specifically, we focus on the nature of local excitable and oscillation events, their spatial couplings leading to propagating waves and the role of active membrane. Instead of arguing for their functional importance, we prefer to consider such patterns as basic properties of dynamic systems. We discuss how knowledge of these patterns could be used to dissect the structure of cellular organization and how the network-centric view could help define cellular functions as transitions between different dynamical states. Last, we speculate on how these patterns could encode temporal and spatial information.

This article is part of the theme issue ‘Self-organization in cell biology’.

Nodal and BMP dispersal during early zebrafish development

The secreted TGF-β superfamily signals Nodal and BMP coordinate the patterning of vertebrate embryos. Nodal specifies endoderm and mesoderm during germ layer formation, and BMP specifies ventral fates and patterns the dorsal/ventral axis. Five major models have been proposed to explain how the correct distributions of Nodal and BMP are achieved within tissues to orchestrate embryogenesis: source/sink, transcriptional determination, relay, self-regulation, and shuttling. Here, we discuss recent experiments probing these signal dispersal models, focusing on early zebrafish development.